A new approximation theory which unifies spherical and Cohen--Macaulay approximations

DOI10.1016/J.JPAA.2006.03.010zbMath1138.13005arXivmath/0603286OpenAlexW1968674853MaRDI QIDQ861855

Ryo Takahashi

Publication date: 2 February 2007

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0603286

zbMATH Keywords

Cohen-Macaulay ringCohen-Macaulay moduleCohen-Macaulay approximation

Mathematics Subject Classification ID

Module categories in associative algebras (16D90) Structure, classification theorems for modules and ideals in commutative rings (13C05) Syzygies, resolutions, complexes and commutative rings (13D02) Other special types of modules and ideals in commutative rings (13C13)

Related Items (8)

Relative syzygies and grade of modules. ⋮ Some properties of \(n\)-semidualizing modules ⋮ Remarks on torsionfreeness and its applications ⋮ On the existence of embeddings into modules of finite homological dimensions ⋮ Homological invariants related to semidualizing bimodules ⋮ About q-approximations and q-hulls over a Noetherian ring, some refinements of the Auslander-Bridger theory ⋮ Relative torsionfree modules with respect to a faithfully balanced bimodule ⋮ CANONICAL AND -CANONICAL MODULES OF A NOETHERIAN ALGEBRA

Cites Work

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• Homological invariants associated to semi-dualizing bimodules.
• Higher-dimensional Auslander-Reiten theory on maximal orthogonal subcategories.
• Gorenstein dimension and torsion of modules over commutative noetherian rings
• The homological theory of maximal Cohen-Macaulay approximations
• Stable module theory
• An algorithm for computing the integral closure

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